BP: Negligent, but not grossly?

FORTUNE — Three years after BP’s Gulf oil spill, the company must legally prove that it messed up, but it didn’t mess up that bad.

BP BP launched its defense on Monday during the seventh week of a civil trial to determine who’s to blame for the 2010 Deepwater Horizon disaster. U.S. District Judge Carl Barbier is hearing the trial in Louisiana. BP’s first witness, Adam Bourgoyne, is a former dean of Louisiana State University’s engineering college and has said that based on his expertise, BP’s management all of the major problems regarding the spill was up to snuff.

BP needs the judge to bite on this. Already, the company has slimmed down considerably since the spill, having divested $38 billion worth of assets since 2010. During the fourth quarter of 2012, it finished its final payment to the $20 billion Trust Fund, mandated by the U.S. government to fund spill-related claims.

But should Justice Barbier find the oil giant grossly negligent, instead of just negligent, BP could have to pay up to an additional $20 billion under the Clean Water Act. Basically, the company will have to prove that a series of bad but somewhat understandable incidents contributed to the explosion on the Transocean-owned and operated Deepwater Horizon rig. But the company must prove that in no way did any attempt to boost profit or shortcut safety procedures contribute to the disaster.

This is a tricky line for BP to walk. Especially since CEO Bob Dudley, who took over in 2010 from PR disaster Tony Hayward, emphasized safety improvements compared to previous years in the company’s 2012 fourth-quarter earnings call. “Turning to safety and risk management,” he said, “some say we are now too attentive to this, but let me be clear — this is good business both for the near-term and the years ahead.”

Dudley did not mention who exactly was concerned that BP was “too attentive” to safety. He did, however, boast a reduction in the company’s Tier 1 safety incidents — Tier 1 incidents being those that involve spills small enough for local operators and contractors to contain. BP had 43 Tier 1 safety incidents in 2012 compared to 74 in 2011. Of course, BP is a much smaller company, following all the divestments in recent years. There are fewer operations to manage and fewer employees at risk.

Now BP must convince shareholders that it is leaner, smarter, and safer than it was, and convince the court over these next two weeks that the company was never that unsafe to begin with.